I'm not in a position to comment on the finer points of your changes to '/etc/inittab'. The way I read it you attempted to modify '/etc/inittab' and ensure persistence via backup (i.e. include 'etc/inittab' in '/opt/.filetool.lst'). I'm pretty certain that will never achieve what you hope for:
AFAIK the restoration from backup happens too late in the boot process to replace the '/etc/inittab' file from the initrd (i.e. 'tinycore.gz') with your modified version. IIRC the restoration is done via '/etc/init.d/tc-restore.sh' which gets called almost at the very end of the execution of '/etc/init.d/tc-config'. Unfortunately the restoration takes place before you get access to the system, and when you (after the boot process is complete) look at the file content you'll probably see the modified content. That is when you start scratching your head ...
Therefore the only way I imagine that you achieve a different outcome would be via
remastering of the initrd (and if you boot using a CD-ROM also
remastering of the ISO image).
If you take a look at '/init' you'll find that the 'multivt' boot code actually does a change of the '/etc/inittab' content by overwriting it with '/etc/inittab-save'. All this has to happen befor '/sbin/init' is called. Therefore I'd suggest you modify '/etc/inittab' and NOT use boot code 'multivt' (or change '/etc/inittab-save' if you want to continue to use boot code 'multivt').